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stodd9503
18.07.2019 •
Mathematics
Use stoke's theorem to evaluate∬m(∇×f)⋅ds where m is the hemisphere x^2+y^2+z^2=9, x≥0, with the normal in the direction of the positive x direction, and f=⟨x^5,0,y^1⟩. begin by writing down the "standard" parametrization of ∂m as a function of the angle θ (denoted by "t" in your answer)
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Ответ:
where
where
We can check this result by evaluating the equivalent surface integral. We have
and we can parameterize
so that
where
as expected.
Ответ:
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